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Quiz_2_20C

# Quiz_2_20C - θ it subtends with the formula A = 1 2 r 2 θ...

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Math 20C (Shenk). Quiz 2. August 23, 2010. Name Work alone and use no books, notes, or calculators. Put your work on 8.”‘ × 11” paper and staple it to the quiz when you turn it in.‘ 1. What is the curvature at x = 0 of y = e 2 x , oriented from left to right? 2. When an object is at (5 , 5) in an xy -plane with distances measured in feet, its velocity vector is 3 i + 4 j feet per second, the curvature of its path is - 2 feet - 1 and it is speeding up 5 feet per second 2 . What is its acceleration vector at that time? 3. (a) Based on the level curves of z = L ( x, y ) in Figure 1, what is the approximate value of L x (20 , 10)? (b) What is the approximate directional derivative of L at (20 , 10) in the direction toward the origin? 4 3 2 1 x 20 - 10 y 20 r θ FIGURE 1 FIGURE 2 4. Give a formula for the linear function z = M ( x,y ) with the values M (1 , 1) = 10 , M (6 , 1) = 30, and M (1 , 6) = 0. 5. The area of a sector of a circle (Figure 2) is calculated from its radius r and the angle

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Unformatted text preview: θ it subtends with the formula A = 1 2 r 2 θ . The radius is measured to be 2 inches with an error ≤ . 02 inches and the angle is measured to be 0 . 5 radian with an error ≤ . 001 radian. (a) Give an equation of the tangent plane to A = 1 2 r 2 θ at r = 2 , θ = 0 . 5. (b) Use the tangent plane to estimate the maximum error in the calculated area. 6. What is the maximum directional derivative of H ( x,y ) = x 2 + y 3 at (3 ,-1)? (OVER) Scores: 1 2 3 4 5 6 7 8 Total 1 Math 20C (Shenk). Quiz 2 p. 2 7. A rectangular box (Figure 3) is to have of volume of 1 cubic foot. What dimensions should it have to minimize the total area of its six sides? (Use calculus.) y x z FIGURE 3 8. Find the critical points of f ( x,y ) = xy + y 2-3 y and use the second-derivative test to classify them....
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Quiz_2_20C - θ it subtends with the formula A = 1 2 r 2 θ...

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